Theoretical Advances From the QRANGE Framework

Quantum theory contains a form of randomness that is not the result of ignorance or any stochastic behavior. For instance, according to the theory, if we prepare an electron with a definite value for its spin in the Z direction, measuring it along the X direction will give a fully unpredictable result. This is despite the fact that the description of the experiment within the theory is complete, in the sense that the prepared state and implemented measurement are perfectly known, without any stochastic component. This form of randomness is intrinsic to quantum theory and impossible in classical physics. Beyond fundamental considerations, it is also the key element behind any quantum random-number generator (QRNG).

In real life implementations, however, neither particle sources nor measurement devices are perfect. Different sources of noise introduce an unavoidable element of stochasticity that produces an apparent randomness that is not intrinsic to quantum theory. Therefore, it is a fundamental problem to design the tools to estimate the correct amount of intrinsic quantum randomness produced by a quantum device.

The natural and operational way to model the stochasticity in the components of a device is through classical or quantum correlations with an external observer, Eve, who can also be interpreted as an eavesdropper and whose goal is to make the best guess about the device’s outcomes. The logarithm of Eve’s maximum guessing probability, i.e., the conditional quantum min-entropy[1], characterizes the amount of intrinsic randomness in a quantum measurement’s outcome.

The European research project QRANGE, of which Quside was an industrial partner, had amongst its main goals the development of a framework to precisely quantify the amount of conditional quantum min-entropy generated by a quantum device (particularly, by QRNGs). As a result of the efforts therein, last year a paper in collaboration with researchers from the Institute of Photonic Sciences (ICFO) and from Bosch’s R&D department was uploaded to the arXiv, putting forward the theoretical underpinnings for the said framework.

With respect to the previous state of the art, the contributions of this new work were twofold. On the one hand, it highlighted the importance of a correct modelling of the nonidealities in the measurement device (something that, remarkably, was often not done). On the other, it showed that if the measurement device has a (potentially hidden) quantum memory, entanglement generation between itself and the measured device must be taken into account for a proper estimation of the generated quantum entropy. You can check the technical details in the manuscript and, if you are attending QIP 2023, you can come by the poster session on Monday where I’ll be explaining the main results.

During the following months, we will be working on integrating this new theoretical framework with our Randomness Metrology Suite. These efforts will be supported by the Spanish Research Agency, within the “Ayudas Torres Quevedo” program. Stay tuned for exciting developments to come!

[1] Check out our previous post about quantum entropy.